Sometimes people say that water is removed from clothes ibghvk 4/ /8 g:fy1fhh7/vkzwvn a spin dryer by centrifugal force throwing thez h:fyk/4/ g1bhv7 fgkvv 8h/w water outward. What is wrong with this statement?

Will the accelerationvm:v0g(i c6sc of a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gmgsi:0v (vcc 6entle curve at the same speed? Explain.

Suppose a car moves at 8p x.3pms268 mf vop oksw9z*qconstant speed along a hilly road. Where does the car exert the greatest and leastpzsxp6k3o8* vm2. oq8m s9wfp forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-giye , af:( xono6wya2t/- bvx13(ne cmo-round. Which of these forces provides the centripetal acceleration ofw yx o3(i ncbn(ayet6,v 1xo2 -me:f/a the child?

A bucket of water can be whirled in a vertical circle without the w2qm 6q12 bdvqyater spilling out, even at the top o dvqq bm26yq21f the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are abnga6gfxj :/q /8rps4xpm0osx *l1 0qt least three controls in the car whis /a: xxb rg0jmq gppn6q1*xl4o8/s0fch can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes vcdg 8n7wge 3efh.c.,flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not afgg.8h.e7cwc ne,v 3 dchieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve mks/ -x6j:daek gk 56sat high speed?

Why do airplanes bank when they turn? How would you comput6n:rf05bgj jv e the banking angle given its speed and radius of :5j6jnfrb0gv the turn?

A girl is whirling a ball on a strin(1zmp66+hka7 jvyvyn g around her head in a horizontal plane. She wants to leth6z7yvy+akm j6 (np v1 go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large at/mv3qtyhzru.b 00-4 w yr whbs-2y7z force? Consider an -s z3w mh0u .ywh/q04rb7y 2vybtrtz-apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’, n3cm b/dekpqlx hb7v1l67- ps orbit be dik7/ ml3n -,7q pec x6dpvl1hbbfferent?

Which pulls harder gravitationally, the Earth on the Moon, ok 4zgvoy ,: 0abztmr4e b8gl4.r the Moon on the Earth? Which accelery.vb4tkb8 o e 4 g,:mz04azrglates more?

The Sun's gravitational pk0zca5+nrzv 19z:e leull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from olr :a1enkv0czz +ze5 9ne side of the Earth to the other.]

Will an object weigh more at syn0 m4 i ny;j6 )iik:y7ga2jzthe equator or at the poles? What two effects are at work? Do they oppose each oth02ngns j;kij) ii7yyz4a: ym6 er?

The gravitational force on the Moon due to the Ear46j*ulxx9v o wth is only about half the force on the Moon due to the Sun. Why iso v*l9 u4j6wxxn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars iz 9la2uqi; xiko.u w.-n its orbit around the Sun larger or smaller than the centripetal acceleratio azx uk29w.il;uoqi. -n of the Earth?

Would it require less speed tu8p*w( b2k )ua:(muz pce5wi:btgc*ro launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation d2bruktecb*8wucga: p uw5:m*( p)z(i irection.

When will your apparent weight be the great1h8el t c/ ;cwibcs/,qest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which cas8/c;ht1wsec q/l,ic be would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could mfts-y7n +gcva8 *ckf3jd;-jbe adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates graviakgj8t* cnd-y fs3m7-cjvf +;ty. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “app )0m(p3cj pdl1m:dcvd arent weightlessness” between s 0c mcvpmjdp)ld3 d1(:teps.

The Earth moves faster in its orbit around the Sun in January than in Julo8s6d .rbz4ds y. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane4ro s d8s.6dbz of its orbit.]

The mass of Pluto was not known until it was discovered to sfgrx,:;swb2pdy4 h4 have a moon. Explain x4;gfb4r yp2: w,dhs show this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger t6t+jxr m: +e6r zrtk+rhan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with +6t+r+emkx6ztr :r rja speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 198ff wc nw5 -w/7xmfwsym: /r9o3gh,ye +0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit arju9s 8t s(vbfaaqkef;q+ )/x.ound the Sun, and the net force exerted on the Earth. What exerts this force on the Efbaqj)sk9sv/x.8uaqf e+(;tarth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotate6 4* 9ldzscmids uniformlycm zs*d4d6i l9 in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is ( gc,h*q42sn ch9*punu *bgdzin orbit 400 km from the Earth's surface, and circles the Ear z,hqgd4g(*upc*n bn 2* uc9shth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of ib4tw ,ymq+o gb8h4+aa potter’s wheel 4 ow+yb+,mh8tqabi g 4turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved nnh20t0ls -uu83-jn ap 7oskxat a uniform rate in a vertical circle of radius 72.0 cm , as lo-a-kshtuun n08 7n 23jxs0pshown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed 2i t;2+g jfmyqkqj5y8with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independeng+qijy jf5k;qm8 t 2y2t of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the rc -oih ifwrju 3+ 5.(l2ki+jejoad if a car isi5.jr+l -if(ejuwcj 2 h3oki+ to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronau r yep1.c43z6f1cq jdxts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own wei1dpr46fec 1 jqz3.c yxght, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of vary7ci)u) /ywxil hpo1+j;q 2bfiable speed. When the speed of the turntable is slowly increased, the coin remains fixepb7 +iyi;y1hj/ qc2l wuxof)) d on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed ,8s+7n c vgrlnmust a roller coaster be traveling when upside down at the top vc, n7+r glsn8of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the roun1plhfs9lkp)u/ j3)oqded top of a hill (radius )h)kj3l u9flo/ pqs1p =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wh :iq;rrsyfs,s(pgmiptwoq7. w2s8 : ed6 z;-heel need to make for the passengers tor-t o qew.si,pwrdm8s:siy( sq:;2z 6pg7; fh feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1. i3mobu- jl+tva48v+o6xdg 6d 10 m. At the lowest point of its motion the tensiotjudi36 +avol4 ox-v8 m+d6gb n in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge r. 7ny5rvj 1s8pcohef0p v4( ieotate if a particle 9.00 cm from the axis of rotation is to ejf5s.0 e y8(nopci7 p1 e4rhvvxperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carniv1befubr;49/ tfxp6pv)x xh2q al, people are rotated in a cylindrically walled "room." ( fh)x u/x14v6bq9rpbx2p ef;tSee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotat7 0oxgi0yrlo4 ed in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to l 0o70yig4rxoa dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight g7l u)(:fz ny2y ;twewsyv98pof the ball which revolves on a string 0.600 m lony;eg) tu ps(z f2y9nyw7vl8 w:g. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked fobxyy 9g9jxs-vx8n0(4o cg,bvr a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses/spk;e -thvtxh i(82r7th3;ta: re fk $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vert gx4wnk(g1cp2v) a; j*/xafuyically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net ,xh: r vxoy:wq:+u8w 6f qp.u1yimk +bforce exerted on the car (by the ground) in Example 5-8 when its u u.bi,81qv+wr+ wxym:hp qy: kxfo6:speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates unifoc mfx*k 24*iymcp/cj /rmly from the pit area, going from rest to 320km/h in a semicircular arc with a cf*ji/y2 mpc4*mcxk/radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of ( wg h b 7n9bkrez4oell,.u;w0radius 2.90 m . At a particular instant, its acceleration is 1.05 zu407( ler,nw wbk.9bohgle ; $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (:zhk;3ueo v*d 2 Earth radii) above the Earth’s skd;* ho:vzu3eurface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratio l;/t3ud:x efon g has a magnitude of 12 m/s;/uld otx:e f3$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravi7f:sh8bqa i dk(im2 p1ty on the Moon. The Moon's radius is 1.7i1spm7kaf:bh(id2 q 84 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, bu:jud9mpok/d; t has the same mass. What is the accelkuo:9 jd pd/;meration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the samew/: v+u(0zpweri9fa n radius. What is g e(aw wruz0/:9f+ nivpnear its surface?   

  Two objects attract each other gravitationally with a fordiv ,b2dw 76ywce of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective valu. gtnt7qpav(g ;5mbeo3hg-* a e of g , the acceleration of gravity, at (a) 3200 m tgpe3aha - b 5(n. q*;g7tmvgo   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cepgjqo e 0y;pgxf7s;s1d8w:6bnter to a point outside the Earth where thegravitational acceleration due to the Earth i q o7ysj:s gp; f61g8eb0wxdp;s $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star h ibjk,jh pb.. 3jgb)lpnpb.4;m ,0nywas five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster. )3 j4jwyk.m p,b i; bppjbnn,g.lb h0.   $\times10^12$

  A typical white-dwarf star, which once was an y bctho,)dyb +-4b q.zaverage star like our Sun but is now in the last st-+)b.bdhb y,ty4qoc zage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless whil6kgph.yz ao om1;ikry -6i*0te orbiting in the space shuttle. Your friendsy ypht10m;* .6or6kgaiko -i z respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squarevx4 p,h:h(uu)x8tm kp of side 0.60 m. Calculam(ptupxx:u )kh8,h v4te the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on theiz7 24qehy(u 1bj h4wv same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (F1vhyzbi(24qejhw u 47ig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity ajy: gx xx6l oe -5mjz5ju81j/xt the surface of Mars is 0.38 of what it is on Earth, and 16gj-x xl5zojx m: 58ejuj/yxthat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun uq ;+ tzxazu),w bcs.hgrr /2()ut)qnusing the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained usi)tutnrg/ q ;) x+u zba(rhsw zq),u2c.ng Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a q4 ls 4hco9ly/l,vvhe 63 g*3ti8ayr+ndpr/istable circular orbit about the Earth at a hetdyphqr,ov nv9 // +48* si3lclih6yr3 ag4leight of 3600 km.    $\times 10^3$

  The space shuttle releases a sate4nm:qfc3q ;,lz com7 dllite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (r nd:ccm;,fm3qozl7 q4elative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if oc+30biyqzx9 pps1 khf *cupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Qz03shf qxk1p y b*ip9+uestion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to oz(e1zc1s -ao lc(dp5 srbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the pc-z a1c(s1(5zd soelradius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellityl,z ,h+ykd .jg32al ae have to be launched from the top of Mt,l ,2jly.3+kag dayzh . Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunasejcyb 5 d955zr landing mission, the command module continued to orbit the Moon at an altitude of about 19e555bzd yj cs00 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Ty:7fjgp+ dc5phe innef+5: gp ypj7cdr radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m hn:/tw 0 kq-v.okfo e0in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the n0 :o/kthv.of0weqk -top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 witb, ,.d oh99k1 7c)rzxncqh km from the center of the Earth's Moon in a space vehicle (a) moving7icw1h 9d.hk )9 z qob,rxnct, at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system c7 8h- s5fd mvi3li:nyzonsists of two stars of equal mass. They are observed tzi n7 lm-:yh8fv5s3 ido be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in l )62spcna bx lz61a8zk1y+hqan elevator that movesaqzk+ap6c6)81x 2b ll1y nh sz
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord susrs ,pmbder :88pended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? asmr:d8br8 ep , =   

Show that if a satellite orbits very nek8t4 6:q q tlo ozim1a);k,b4 epg0pvzacse63ar the surface of a planet with period T , the density (mass/volume) of theom, at86qo4zlcq 6epze;b ki)p1 t40v:3kga s planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to 5 jlhjbb1a a(,determine the period of an artificia 1 bh(ba,la5jjl satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits thed + j6o..uphu.+qq4**kkpnvz rnksw5 Sun like the planets. Its period is 410 duspwk+jd4p+q o* n uk*5 h..qn 6.rvkz. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average d)fd yj sd5p90 otkn*8,wef hl8istance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very close t: (.oowuo7u9b 2aeuubo the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nao oue(2 o97.wuuub:bearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about th huou s4lgf04x(:zbv)z p+i*be center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for thtk2x*ac v:-i te four largest moons of Jupiter* cv :itatx2-k (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass ofev 8rm6tztj8w5u xff 7 1+g5ei the Earth from the known period and distance of the Moon. 7grtu6x m+ v5ff8w5zjte 1e8 i   $\times 10^{24}$

  Determine the mean distance from Jupiter for:1-v/xgnw 2 vlojy/py djd96r each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values invwj-dlr1xvg2//y :yj pon 96 d the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and l )be)pn zvgm8)mx*0g Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sum0lgnb)v)*zp) e8m gxn but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "pla.c-bg uer02 nknet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it isgu2nc er0.k- b always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swingi,+ 1ytrxcyfg:rp(t ui :7 +nlgng in an arc from a hanging vine (Fig. 5–41). If his arms at 7,(:+ n xugl1g ty:fi+rpycrre capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface w jf,pcpsr9fv6q+jk 5 7ill the acceleration of gravity be half what it is on the surfacf, c6+jp jp9qv7k5f sre?    $\times 10^6$

  On an ice rink, two ywwdl7i *4rb05 i wrw.skaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are eacw7ywr0wliw dr. b5 4*ih 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accel..cnqwi6erpw pm5q 5 3eration of gravity at the wq nq56rwp.ie3cpm.5 equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from th a6su:isz1jqh.g; g j +a5weo 1msn34ne Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull 1naqjie+zhw4og. 31n s; jm: sagu s65with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an e3 uaf6 puzry:*levator, it says your mass is 82 kg. Wha p3f:ur6 u*ayzt is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that, ,tx tdafkml )1o.*w/ujnr/h will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must1fu.jdhn/m,,t/ otwrlx k)a * be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft inh6rxj81;k kw l a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its fkx,r ip)y57gc*goo5radius r, the acceleration dk*xo )y5p,g 5o7gcrifue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from thu7cel u, )rcc.e vertical by an eu7 rccl)uc, .angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is .fs k;gk1z c i*y2d.ambanked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range z kcsk1y;.2d*gafi. mof speeds can a car safely handle the curve?

  How long would a day be if the Eajjyy-k p;yr, nobom; /x*bbl v4 in,)-rth were rotating so fast that objects at the equator were apparently we b)bi r4 /y n;j;ym bxvo,-n,lkoy*jp-ightless?    $\times 10^3$s

  Two equal-mass stars maintain a chhra ajp 5.2w/d(1 hh 4cc8vg9ci(a f-kta0zronstant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant spea0il 8u73f(syq7l nop ed rounds a curve of radius 235 m. A lamp suspended from i(n 7plyf3 a7 us0o8qlthe ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus.kouf.v+5e;xfodur 9 , it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter:k d;fxo5 uufv .o9.er+ mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an kep49isw ft: 3 8fzt9mextremely massive core in the distant galaxy M88iwpttsf9mz34:f9 k e7, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed cwb(l ji0r-bmn k; d*mg03hn. as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c)*r;b0 nmi k h0 -.gbmcdjn3lw( How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a gu jgl 9eq.h5bop b;:v/roup of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nauticah.pv;l/5g9q:bebj o ul ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvousb+6 i +*octx.pbz7bwd (NEAR), after traveling 2.1 billion km, is meant to orbit the aste6+bbi 7x +zcdtp*owb .roid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shut7og; vnaqa j)2tle pursuing a satellite in need of repair. You are in a circulg aq7a jv;)on2ar orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 yearsi 4 c34jn 154ur0qs ui5tbkpti. (a) What is its mean distance from the Sun? tit u345 qrin b45c puj0s1ik4  
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the va2f6a86pgl ksy9t jpk+so j -c2lue of G would need to be if you could actually "feel" yourself gravitationa-2 2g8lfo cjspk6t6skj+ap y9lly attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. m -igwnk-c3es;w ry.t5f;-m h5-46) at a distance of about 30,000 light-years from the cen;sghm f mce3-;ywr-k 5t.n-w iter $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a squafik wb4h/a8 u0qtv)5ajv:y) nx ass.+ re 0.50 m on each side. Find the magnitude and directisjb5wvq+uanai0v) xk4)sha .8 y f t:/on of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth .mk 6hoi01pnn $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the accelerati5zz6iiszy- w t bx;25b5ys3f aon experienced by the tip of the 1.5-cm-long sweep second hand on your wrist watcaw yz5-sbbs;2z fy zti 6i5x35h?    $\times 10^{-4}$

  While fishing, you get bored and start+ ehd8foep :ldx5ck6)r)cyf: to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight make::ekxdo r 8efyp df +65lh)c)cs a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in;sn m c24ep5tpejkj ,) a new highway is designed so that a car traveling at sk)nt;ee4j ps m pj,c52peed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acei(m cdpj( p3.fla, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the m3 fp .(pc(idjtrack is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$